Results 21 to 30 of about 164 (68)
Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Let K be a nonempty compact convex subset of a topological vector space. In this paper‐sufficient conditions are given for the existence of x ∈ K such that F(T)∩VEP(F) ≠ ∅, where F(T) is the set of all fixed points of the multivalued mapping T and VEP(F) is the set of all solutions for vector equilibrium problem of the vector‐valued mapping F.
Kanokwan Sitthithakerngkiet +2 more
wiley +1 more source
MathematicsThe primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme.
Habib ur Rehman +3 more
doaj +1 more source
Auxiliary problem principles for equilibria [PDF]
, 2016 The auxiliary problem principle allows solving a given equilibrium problem (EP) through an equivalent auxiliary problem with better properties.
BIGI, GIANCARLO, PASSACANTANDO, MAURO
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Journal of Applied Mathematics, Volume 2012, Issue 1, 2012., 2012 We introduce the new iterative methods for finding a common solution set of monotone, Lipschitz‐type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space.
Rabian Wangkeeree +2 more
wiley +1 more source
Advances in Operations Research, Volume 2012, Issue 1, 2012., 2012 We introduce the notion of relaxed (ρ‐θ)‐η‐invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational‐like inequality problems with relaxed (ρ‐θ)‐η‐invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of (ρ‐
N. K. Mahato +2 more
wiley +1 more source
Convergence of Adaptive Algorithms for Equilibrium Problems in Hadamard Spaces
Journal of Optimization, Differential Equations and Their ApplicationsIn this paper, we consider the equilibrium problems under the setting of Hadamard spaces. For an approximate solution of equilibrium problems, iterative adaptive two-stage proximal algorithms are proposed and studied.
Serhii V. Denysov +2 more
doaj +1 more source
On Penalty and Gap Function Methods for Bilevel Equilibrium Problems
Journal of Applied Mathematics, Volume 2011, Issue 1, 2011., 2011 We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one‐level ones. We generalize a pseudo‐∇‐monotonicity concept from ∇‐monotonicity and prove that under pseudo‐∇‐monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem ...
Bui Van Dinh, Le Dung Muu, Ya Ping Fang
wiley +1 more source
Contraction-mapping algorithm for the equilibrium problem over the fixed point set of a nonexpansive semigroup [PDF]
, 2019 In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive.
Le Qung Thuy, Trinh Ngoc Hai
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Mixed quasi invex equilibrium problems
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 57, Page 3057-3067, 2004., 2004 We introduce a new class of equilibrium problems, known as mixed quasi invex equilibrium (or equilibrium-like) problems. This class of invex equilibrium problems includes equilibrium problems, variational inequalities, and variational‐like inequalities as special cases.
Muhammad Aslam Noor
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First Order Characterizations of Pseudoconvex Functions [PDF]
, 2001 First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed.
Ivanov, Vsevolod
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